Successful in the "business sense":
An marketable cast of characters
The ability to hook Kids 6-11
The marketing muscle of a big, veteran company like Disney or Nickelodeon
Decent time slots
The ability to find it's groove early on (stay one way for most of it's run, not a lot of experimentiation)
In certain cases (like South Park, Family Guy, the Boondocks) the ability to attract controversy onto itself
Successful in the sense of the actual cartoon
An appealing cast of characters
Good writing
A healthy sense of creativity
A minmum of needless executive interference